Chapter 12.7, Problem 23E

To determine

To Find : The number of combinations of ${}_{25}{C}_3$

Answer to Problem 23E

The number of combinations of ${}_{25}{C}_3$ is $2300$ .

Explanation of Solution

Given information :

Consider the information provided in the question.

Formula used :

  $nCr=\frac{n!}{r!(n-r)!}$

Calculation :

Use the formula provided above to find ${}_{25}{C}_3$

  $\begin{array}{l}nCr=\frac{n!}{r!(n-r)!}\\ {}_{25}{C}_3=\frac{25!}{3!\left(25-3\right)!}\text{ [use combinations formula]}\\ =\frac{25\cdot 24\cdot 23}{3\cdot 2}\text{ [write as products and divide out common factors ]}\\ =\text{ 2300 [multiply]}\end{array}$

The number of combinations of ${}_{25}{C}_3$ is 2300